Such process for producing methanol is known for instance from EP 0 790 226 B1. The methanol is produced in a cyclic process, in which a mixture of fresh and partly reacted synthesis gas is first supplied to a water-cooled reactor and then to a gas-cooled reactor, in which the synthesis gas is each converted to methanol on a copper catalyst. The methanol produced in the process is separated from the synthesis gas to be recirculated, which then is passed through the gas-cooled reactor as coolant and preheated to a temperature of 220 to 280° C., before it is introduced into the first synthesis reactor. The maximum yield of methanol in the gas-cooled, second reactor, which is determined by the thermodynamics, greatly depends on the temperature profile in the reactor and on the outlet temperature thereof. If the water-cooled first reactor is filled with fresh catalyst, a large part of the carbon oxides in the water-cooled reactor is converted. However, the amount of carbon oxides converted in the water-cooled reactor decreases with the ageing of the catalyst, which leads to the fact that a large part of the total conversion of methanol takes place in the gas-cooled reactor. In order to counter the effect of ageing of the catalyst in the water-cooled reactor, the outlet temperature from the first reactor and hence the inlet temperature into the second reactor is increased. An increase in temperature, however, causes a shift of the reaction equilibrium towards the educts in the gas cooled reactor, which means a reduction of the maximum methanol yield to be achieved.